On higher extensions of quiver representations over F1

2026/06/02 by Changjian Fu, Liang Yang, L Yang +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics

paper · pdf · doi:10.1080/00927872.2026.2693621

Abstract

We show that higher extension spaces between finite-dimensional nilpotent F1-representations may be infinite-dimensional, thereby clarifying a misconception in the literature. Our examples arise from cyclic quivers. In particular, for a cyclic quiver Δn, we show that Ext3(−,−) vanishes for any pair of finite-dimensional nilpotent F1-representations of Δn, while Ext2(−,−) is infinite-dimensional for any pair of nilpotent simple representations.

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